January 9 – Martyrs' Day: Armed clashes between United States troops and Panamanian civilians in the Panama Canal Zone precipitate a major international crisis, resulting in the deaths of 21 Panamanians and 4 U.S. soldiers.

Pope Paul VI institutes the World Day of Prayer for Vocations. During this celebration the Pope reminds the universal Church that still today salvation comes to everyone. It continues to be celebrated every Fourth Sunday of Easter also known as Good Shepherd Sunday.

February 5 – India backs out of its promise to hold a plebiscite in the disputed territory of Kashmir. In 1948, India had taken the issue of Kashmir to the United Nations Security Council and offered to hold a plebiscite in the held Kashmir under UN supervision.

February 26 – U.S. politician John Glenn slips on a bathroom rug in his Columbus, Ohio, apartment and hits his head on the bathtub, injuring his left inner ear, and prompting him (later that week) to withdraw from the race for the Democratic Party Senate nomination.

February 29 – U.S. President Lyndon B. Johnson announces that the United States has developed a jet airplane (the A-11), capable of sustained flight at more than 2,000 miles per hour (3,200 km/h) and of altitudes of more than 70,000 feet (21,000 m).

March 26 – U.S. Defense Secretary Robert McNamara delivers an address that reiterates American determination to give South Vietnam increased military and economic aid, in its war against the Communist insurgency.

Sentences totaling 307 years are passed on 12 men who stole £2.6m in used bank notes, after holding up the night mail train traveling from Glasgow to London in August 1963 – a heist that became known as the Great Train Robbery.

April 19 – In Laos, the coalition government of Prince Souvanna Phouma is deposed by a right-wing military group, led by Brig. Gen. Kouprasith Abhay. Not supported by the U.S., the coup is ultimately unsuccessful, and Souvanna Phouma is reinstated, remaining Prime Minister until 1975.

The 1964 New York World's Fair opens to celebrate the 300th anniversary of New Amsterdam being taken over by British forces under the Duke of York (later King James II) and being renamed New York in 1664. The fair runs until October 18, 1964, and reopens April 21, 1965, finally closing October 17, 1965. (Not sanctioned, due to being within 10 years of the Seattle World's Fair in 1962, some countries decline, but many countries have pavilions with exotic crafts, art and food.)

Senator Barry Goldwater receives more than 75% of the votes in the Texas Republican Presidential primary.

Some 400–1,000 students march through Times Square, New York, and another 700 in San Francisco, in the first major student demonstration against the Vietnam War. Smaller marches also occur in Boston, Seattle, and Madison, Wisconsin.

Mrs. Madeline Dassault, 63, wife of a French plane manufacturer and politician, is kidnapped while leaving her car in front of her Paris home; she is found unharmed the next day in a farmhouse 27 miles (43 km) from Paris.

August 27 – Walt Disney's Mary Poppins has its world premiere in Los Angeles. It will go on to become Disney's biggest moneymaker, and winner of 5 Academy Awards, including a Best Actress award for Julie Andrews, who accepted the part after she was passed over by Jack L. Warner for the leading role of Eliza Doolittle in the film version of My Fair Lady. Mary Poppins is the first Disney film to be nominated for Best Picture.

October 12 – The Soviet Union launches Voskhod 1 into Earth orbit as the first spacecraft with a multi-person crew and the first flight without space suits. The flight is cut short and lands again on October 13 after 16 orbits.

October 21 – The film version of the hit Broadway stage musical My Fair Lady premieres in New York City. The movie stars Audrey Hepburn in the role of Eliza Doolittle and Rex Harrison repeating his stage performance as Professor Henry Higgins, and which will win him his only Academy Award for Best Actor. The film will win seven other Academy Awards, including Best Picture, but Audrey Hepburn will not be nominated. Critics interpret this as a rebuke to Jack L. Warner for choosing Ms. Hepburn over Julie Andrews.

Canada: A Federal Multi-Party Parliamentary Committee selects a design to become the new official Flag of Canada.

A 5.3 kiloton nuclear device is detonated at the Tatum Salt Dome, 21 miles (34 km) from Hattiesburg, Mississippi, as part of the Vela Uniform program. This test is the Salmon phase of the Atomic Energy Commission's Project Dribble.

October 24 – Northern Rhodesia, a former British protectorate, becomes the independent Republic of Zambia, ending 73 years of British rule.

Berkeley Free Speech Movement: Police arrest about 800 students at the University of California, Berkeley, following their takeover of and massive sit-in at the Sproul Hall administration building. The sit-in most directly protested the U.C. Regents' decision to punish student activists for what many thought had been justified civil disobedience earlier in the conflict.

The Danish football club Brøndby IF was founded as a merger between the two local clubs Brøndbyøster Idrætsforening and Brøndbyvester Idrætsforening. The club has won the national championship Danish Superliga 10 times, and has won the national Danish Cups six times since the club joined the Danish top-flight football league in 1981.